Answer:
1) ![y=(x-1)^2+4](https://tex.z-dn.net/?f=y%3D%28x-1%29%5E2%2B4)
2) ![y=-2(x+1)^2-9](https://tex.z-dn.net/?f=y%3D-2%28x%2B1%29%5E2-9)
Step-by-step explanation:
The equation of the parabola in the vertex form is
![y=a(x-h)^2+k,](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk%2C)
where
is the vertex of the parabola.
1) Given:
![y= x^2-2x+5](https://tex.z-dn.net/?f=y%3D%20x%5E2-2x%2B5)
Rewrite it as
![y=x^2-2x+1+4\\ \\y=(x-1)^2+4](https://tex.z-dn.net/?f=y%3Dx%5E2-2x%2B1%2B4%5C%5C%20%5C%5Cy%3D%28x-1%29%5E2%2B4)
2) Given:
![y= -2x^2-4x-11](https://tex.z-dn.net/?f=y%3D%20-2x%5E2-4x-11)
Rewrite it as
![y=-2x^2-4x-2-9\\ \\y=-2(x^2+2x+1)-9\\ \\y=-2(x+1)^2-9](https://tex.z-dn.net/?f=y%3D-2x%5E2-4x-2-9%5C%5C%20%5C%5Cy%3D-2%28x%5E2%2B2x%2B1%29-9%5C%5C%20%5C%5Cy%3D-2%28x%2B1%29%5E2-9)
8/8 or 1 from 2/4 converting to 4/8 plus 4/8
Answer:
5
Step-by-step explanation:
To solve with calculus, distance is the integral of speed:
d = ∫ |v| dt
d = ∫₀⁴ |t − 3| dt
d = -∫₀³ (t − 3) dt + ∫₃⁴ (t − 3) dt
d = ∫₀³ (3 − t) dt + ∫₃⁴ (t − 3) dt
d = (3t − ½ t²) |₀³ + (½ t² − 3t) |₃⁴
d = [ (9 − 9/2 ) − (0 − 0) ] + [ (8 − 12) − (9/2 − 9) ]
d = 9/2 + 1/2
d = 5
You can also find this geometrically. Graph y = |x − 3|, then find the area under the curve. You will find it's the area of two triangles.
d = ½ (3)(3) + ½ (1)(1)
d = 5
It's important to note that distance is not the same thing as displacement. Displacement is the difference between where you start and where you stop. Distance is length of the path you take.
next simplify, or reduce, the fractions by removing common factors. Then multiply the numerators, and multiply the denominators. Simplify, or reduce the answer if possible.
...
How to Multiply Three Mixed Numbers
Change all mixed numbers to improper fractions. ...
Reduce the fractions. ...
Cross out any common factors.
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